The present invention relates to a method for measuring unbalanced wheels of an automotive vehicle, more particularly to a method for measuring unbalanced car wheels by means of examination of two points located under an imaginary axis line connecting both centers of the right and left car wheels.
Generally speaking, there are two ways of measuring unbalanced car wheels during rotation of same. One way is a so-called "off the car" system whereby the wheels must be taken off the car for measurement and the other way is a so-called "on the car" system whereby measurement is carried out on the spot without detaching the wheels from the car. The former way, that is the "off the car" system has a merit of high accuracy for detecting an unbalanced wheel itself, but when the wheel is attached to the car again, some difference in wheel axis alignment and axis of a measuring apparatus may occur, so that the "off the car" system may not be satisfactory. On the other hand, the latter way, that is the "on the car" system, has a merit that examination can be carried out without detaching the wheel from the car body, but measurement accuracy according to this system is inferior to the "off the car" system.
There are two types of "on the car" systems, namely, the soft-type and hard-type. An example of the soft-type is shown in FIG. 1A, where a wheel W raised by a jack J vibrates around a point A of a car body due to centrifugal force generated by the unbalanced wheel. The amplitude of the vibration is detected by a detector S and electrically analyzed to display the amount and location of the unbalance.
In the above-mentioned case, it is obvious that the magnitude and location of the vibration are respectively different depending upon structure of suspensions which support the wheels. Therefore, the indicated amount of unbalance may be an approximate value. The position of the attached weight is an intermediate point in the case where forward and reverse rotations of a wheel are carried out in turn. The hard-type is shown in FIG. 1B, where forces f. and -f, generated by an unbalanced wheel are detected by a car-carrying type detector S' with respect to a supporting point B at an opposing wheel. The magnitude of vibration of a wheel according to the hard-type is very small and therefore, the following equation exists with respect to centrifugal force f and detected force R; i.e. EQU R=l.sub.1 /l.sub.2 f
and the suspension structure hardly affects phases because of the hard-type. Therefore, the accuracy of measurement of this case is good, but true correction of a wheel cannot be obtained, because a dynamic unbalance of a rotating body is considered to be a result of at least the following two important dynamic unbalance factors. Namely, one is static unbalance which occurs when the breadth of the rotating body is thin and the center of gravity and the axis of rotation does not coincide with each other. The other is couple unbalance which occurs when the rotating body has a considerable breadth and the center of gravity is on the axis line of the rotating body, but one of the main axes of inertia passing through the center of gravity is declined to the axis of rotation. The so-called dynamic unbalance is, for example, in the case of car wheels, which is a result of the above-mentioned static unbalance and couple unbalance with respect to a rotating body having a considerable breadth.
Taking the respective factors of unbalance into consideration, the hitherto known methods for measuring rotational unbalance providing only a one-point detecting portion according to the "on the car" system is insufficient in principle, as both soft- and hard-type are analyzed as follows referring to FIG. 2.
Assuming that, f.sub.1, f.sub.2 =centrifugal forces due to unbalance,
F=centrifugal force due to correction weight, PA1 R.sub.1 =detected force
then EQU f.sub.1 (l.sub.1 +1.sub.2 +l.sub.3)+f.sub.2 (l+l.sub.2)=R.sub.1 .times.l.sub.1 ( 1)
when a correction weight is mounted, then EQU (f.sub.1 +F)(l.sub.1 +l.sub.2 +l.sub.3)+f.sub.2 (l.sub.1 +l.sub.2)=R.sub.1 .times.l.sub.1 ( 2)
if R.sub.1 =o, then the static unbalance has been considered to be corrected. However, as seen in the above equations of (1) and (2) referring to FIG. 2, the sum of the centrifugal forces merely shows zero. It is obvious that the static unbalance and couple unbalance have not been corrected yet. For example, if we make f.sub.1 =-f.sub.2, then the static unbalance becomes zero, but if we substitute f.sub.2 into the above (1) equation, then we obtain EQU f.sub.1 .times.l.sub.3 =R.sub.1 .times.l.sub.1, EQU R.sub.1 =f.times.(l.sub.3 /l.sub.1)
which, of course, is not zero. This does not mean that we have detected static unbalance.
On the other hand, as for couple force, if f.sub.1 =f.sub.2 then the couple unbalance should become zero, but if we substitute f.sub.2 into the above mentioned equation (1), then we obtain EQU f.sub.1 (2l.sub.1 +2l.sub.2 +l.sub.3)=R.sub.1 .times.l.sub.1 EQU R.sub.1 =f.sub.1 (2l.sub.1 +2l.sub.2 +l.sub.3 /l.sub.1)
which is not zero. This means we have not as yet detected moment unbalance.
From the foregoing description, it is clear that the hitherto known "on the car" system of the balance testing apparatus is a correction system around a supporting point (A or B in FIG. 1A, FIG. 1B), so that it is an insufficient system as the balancing condition is not satisfied.